Study of polymer molecules and conformations with a nanopore

ABSTRACT

The invention features methods for evaluating the conformation of a polymer, for example, for determining the conformational distribution of a plurality of polymers and to detect binding or denaturation events. The methods employ a nanopore which the polymer, e.g., a nucleic acid, traverses. As the polymer traverses the nanopore, measurements of transport properties of the nanopore yield data on the conformation of the polymer.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/918,959, filed Aug. 16, 2004, now U.S. Pat. No. 7,846,738, and claimsbenefit of U.S. Provisional Application No. 60/495,292, filed on Aug.15, 2003, each of which is hereby incorporated by reference.

STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

The invention was made with U.S. Government support under Grant No.0073590 awarded by the National Science Foundation, Grant No.F49620-01-1-0467 awarded by the Air Force Research Laboratory, and GrantNo. DE-FG02-01ER45922 awarded by the Department of Energy. TheGovernment has certain rights in this invention.

BACKGROUND OF THE INVENTION

The invention relates to the field polymer characterization.

Probing, characterizing, and manipulating single polymers like DNA isoften accomplished with the aid of optical methods, e.g., observingevanescent field fluorescence of dye molecules, deflecting light beamsin atomic force microscopes, or trapping attached dielectric objectswith optical tweezers. There has also been remarkable progress at themolecular level in the study of the electrical ionic conduction signalsfrom voltage biased nanoscale biopores. More recently, a voltage bias onan alpha hemolysin biopore has been shown to induce chargedsingle-stranded DNA and RNA molecules to translocate through the pore.Each translocating molecule blocks the open pore ionic current providingan electrical signal that depends on several characteristics of themolecule. This system has limits for studies of biological molecules:the pore is of a fixed size, and its stability and noise characteristicsare restricted by chemical, mechanical, electrical, and thermalconstraints.

Thus, there is a need for new apparatus and methods for studying polymermolecules.

SUMMARY OF THE INVENTION

The invention features methods for evaluating the conformation of apolymer, for example, for determining the conformational distribution ofa plurality of polymers and to detect binding or denaturation events.The methods employ a nanopore which the polymer, e.g., a nucleic acid,traverses. As the polymer traverses the nanopore, measurements oftransport properties of the nanopore yield data on the conformation ofthe polymer.

In one aspect, the invention features a method for determining theconformation of a polymer, including providing an apparatus having amembrane with a nanopore; first and second fluid reservoirs separated bythe membrane and fluidically connected via the nanopore; and a detectorcapable of detecting time-dependent changes in transport properties ofthe nanopore; placing the polymer in the first reservoir; causing thepolymer to traverse the nanopore from the first to the second reservoir;and measuring the transport properties of the nanopore over time,wherein changes in the transport properties over time are indicative ofthe conformation of the polymer. An intervention, as described herein,may also be applied prior to causing the polymer to traverse thenanopore.

The invention further features a method for evaluating the effects of anintervention on the conformation of a polymer, including the steps ofproviding an apparatus as described above; providing transportproperties of the nanopore over time of the polymer in the absence ofthe intervention, wherein changes in the transport properties over timeare indicative of the conformation of the polymer in the absence of theintervention; placing the polymer in the first reservoir; applying theintervention; causing the polymer to traverse the nanopore from thefirst to the second reservoir; measuring the transport properties of thenanopore over time, wherein changes in the transport properties overtime are indicative of the conformation of the polymer in the presenceof the intervention; comparing the transport properties of the nanoporeover time with and without the intervention, wherein the differencebetween the transport properties is indicative of the effect of theintervention on the conformation of the polymer. The intervention may ormay not include a chemical species, e.g., a candidate binding compound,a denaturant, or a nucleic acid. Exemplary non-chemical interventionsinclude a temperature change, light, voltage, or magnetic fields. Thismethod may also be employed to determine changes in conformation causedby altering an existing intervention, without the need for comparison tothe conformation of the polymer in the total absence of a particularintervention.

In various embodiments, the polymer is a nucleic acid (e.g., single- ordouble-stranded DNA or RNA), a protein, a synthetic polymer, or apolysaccharide. The transport property is for example, current,conductance, resistance, capacitance, charge, concentration, an opticalproperty, or chemical structure. The membrane may be a solid statemembrane. The nanopore may also include a biological pore. Thelongitudinal and transverse dimensions of the nanopore may independentlyrange from 1-1000 nm. The polymer may be induced to traverse thenanopore by employing diffusion, electrophoresis, electroosmosic flow,hydrodynamic pressure, magnetic force, optical trapping, mechanicalforce, or a molecular motor. The methods of the invention may berepeated on the same polymer, e.g., wherein in the repetition a nanoporeof different transverse dimension is employed or wherein a differenttype (e.g., change in chemical species, change in non-chemicalintervention, or change from chemical to non-chemical intervention, orvice versa) or extent (e.g., change in concentration of chemical speciesor change in temperature or amount of non-chemical interventionemployed) of intervention is employed.

By “conformation” is meant any non-primary structure of a polymer,including secondary, tertiary, and quaternary structure. A conformationmay be thermally stable or unstable under the experimental conditionsused. Quaternary structure include any specific or non-specific bindinginteractions between a polymer and one or more additional chemicalspecies.

By “polymer” is meant any molecule consisting of two or more monomersand capable of having non-primary structure. Monomers may or may not bechemically identical. For the purposes of this invention, the term mayencompass an aggregate of a polymer and one or more additional chemicalspecies.

By “transport properties of said nanopore” is meant property measurableduring polymer traversal of the nanopore. The transport property may bea function of the solvent, the polymer, a label on the polymer, othersolutes (e.g., ions), or an interaction between the nanopore and thesolvent or polymer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1. Details of the experimental setup. a) TEM image of a ˜3 nmsilicon nitride nanopore. b) Schematic of the apparatus used to obtainelectrical signals from single DNA molecules. c) Characteristic signalsshowing transient molecular current blockades and a baseline currentshift. Parameters t_(d) and <ΔI_(b)> are shown for a selected simplemolecular event.

FIG. 2. Distribution of events as a function of t_(d) and <ΔI_(b)> for10 kbp DNA with a) a 3 nm pore, 2674 events, and b) with a 10 nm pore,9477 events. The bias voltage was 120 mV. The scale represents eventfraction density normalized as a probability distribution so that theintegral of the density over all t_(d) and <ΔI_(b)> is equal to 1.

FIG. 3. Plot of the translocation time distribution function for 3 kbpand 10 kbp DNA molecules in a 10 nm nanopore at 120 mV bias, and for 10kbp DNA at 60 mV bias.

FIG. 4. Density of events over t_(d) and <ΔI_(b)> where plot a) containssimple events characterized by a single blockade level, and plot b)contains the remaining complex events. The inserts show examples ofblockade current time traces of events that contribute to the densityplots. Isolated regions with only one event in a 20 μsec by 2 pA bin arenot displayed in this plot. The scale is the same as in FIG. 2. Thedotted line in b) represents the prediction of equation (1) in the textwith t₀=400 μsec and <ΔI₀>=100 pA.

FIGS. 5 a-5 b. Plots of the instantaneous time distribution of blockadecurrent ΔI_(b) over all events. Current is sampled in a 10 microsecondtime window. The quantized blockade currents corresponding to 0, 1, and2 strands in the pore are clearly seen for 10 kbp DNA data from a 10 nmpore for both (a) 120 mV bias and (b) 60 mV bias.

FIG. 6. Strategy to make nanopores using argon ion-beam sputtering. a)Sputtering removes material from a free-standing Si₃N₄ membrane with acavity. b) Feedback controlled ion-beam sculpting apparatus housed in ahigh-vacuum chamber. a) A 500-nm-thick low-stress (˜200 MPa tensile)Si₃N₄ film was deposited on a (100) silicon substrate by low-pressurechemical vapor deposition. Photolithography and directional wet chemicaletching of silicon were used to create a free-standing 25 μm×25 μm Si₃N₄membrane. Either a bowl-shaped cavity (a), or a single initial pore of˜0.1 μm diameter (not shown), was created near the center of themembrane using, respectively, reactive ion etching or a focused ion beam(FIB) machine. b) A differentially pumped ion gun (VG Microtech modelEX05) exposes the sample surface to an Ar⁺ beam, ˜0.2 μm in diameter. AChanneltron (Gallileo Optics) electron-multiplier style single-iondetector, positioned after the sample, counts transmitted ions.Detection plates at the exit port of the ion gun could detect the beamoff the sample or pulse the ion beam on and off the sample. A focusingEinzel lens and 60° electrostatic detection system between sample anddetector are used to suppress electron, ion and X-ray backgrounds. A50-eV electron gun (Kimball Physics Model FRA-2x1-1) floods the sampleto neutralize surface charging. A liquid-nitrogen-cooled shroudsurrounds the sample and Einzel lens and a quadrupole mass spectrometer,connected to the 10⁻⁹ torr turbo-pumped vacuum chamber, monitorsresidual gas composition. A thermocouple monitors the sample holdertemperature, which is adjusted with cold nitrogen gas and a resistanceheater.

FIG. 7. Sculpting a nanopore. a) Transmitted ion count rate (left axis)and pore area (right axis) versus integrated time the ion beam is on the28° C. sample. b) TEM image of initial 61-nm diameter pore made by FIBin a 500-nm Si₃N₄ membrane. c) TEM image of the same sample after Ar⁺ion-beam exposure. Energy dispersive analysis of X-rays in the TEMreveals the presence of Si and N in the membrane that has filled thepore, although the precise composition has not been quantified. Becausethe transmitted ion current is directly proportional to the area of thepore, the instantaneous pore area indicated in all figures wascalculated by multiplying the initial pore area (determined by TEM) bythe ratio of the instantaneous to initial transmitted ion current.Temperature, 28° C. Flux, 28 Ar⁺ s⁻¹ nm⁻². Duty cycle, 200 ms/1 s.

FIG. 8. Temperature dependence of ion-beam sculpting. Successive datasets at different temperatures (shown) are delimited by their alternateblack and gray coloration. Flux, 14 Ar⁺ s⁻¹ nm⁻². Duty cycle, 200 ms/1s.

FIG. 9. Flux dependence of ion-beam sculpting. Pore area versus totaldose for samples exposed at different instantaneous fluxes, F, to acontinuous beam (gray traces), or a pulsed beam (black traces). Dutycycle, 100 ms/1 s. The plotted black curves overlying the gray datapoints are predicted from the diffusion model under steady-stateconditions (see text). The inset plots 1/X_(m) ² versus flux, from whichD is extracted. Temperature, 28° C.

FIG. 10. Schematic view of a solid state structure surface undergoing amaterial transport and ion sculpting process, identifying physicalmechanisms corresponding to various terms of an ion sculpting modelprovided by the invention.

FIG. 11. Molecular events in a nanopore detector. A Si₃N₄ membrane witha 5-nm pore separated two compartments filled with saline solution (1MKCl, 10 mM Tris-HCl, 1 mM EDTA, pH 8.0). Initially, with only the salinesolution in the compartments, a 120-mV bias between AgCl electrodes ineach compartment resulted in a constant ionic current of 1.66 nA throughthe nanopore. This was consistent with the known conductivity of theionic solution, assuming a pore length of around 10 nm. After addingdouble-stranded DNA, 500 base pairs long, to the negatively biasedcompartment, and allowing time for diffusion, intermittent currentblockades (two are illustrated) were observed. Si₃N₄ membranes withholes of about 100 nm in diameter that were completely closed by ionbeam sculpting produced 20 GΩ seals.

DETAILED DESCRIPTION OF THE INVENTION

A nanometer scale pore, e.g., in a solid-state membrane, enables atechnique in accordance with the invention to probe the structure ofsingle polymers, including those of biological interest in their nativeenvironments. Previous work with biological protein pores wide enough topass and sense single stranded DNA molecules demonstrates the power ofthe nanopore approach to detect linear sequence information andhybridization events, but many future tasks and applications call for arobust solid-state pore whose nanometer scale dimensions and propertiesmay be selected, as one selects the lenses of a microscope.

Methods

The method of the invention observes individual molecules, e.g., ofdouble stranded DNA, and their conformations, e.g., folding behavior,binding, pairing, and hybridization, as they traverse the nanopore. Thenanopore may be described as having longitudinal and transversedimensions. The longitudinal dimensions of the nanopore determine thedistance that a polymer must travel to pass through the pore, i.e., thethickness of the pore. The transverse dimensions of the nanoporedetermine the largest species that can enter the pore, i.e., the widthof the pore. Desirably, the longitudinal dimension of the nanopore issmall enough to restrict the polymer to a discrete set of measurableconformations. The longitudinal dimension is also desirably smaller thanthe conformation being observed. Nanopores useful in the inventiontypically range in transverse dimension from 1-1000 nm, e.g., at most750, 500, 400, 300, 250, 200, 150, 100, 90, 80, 70, 60 50, 40, 30, 20,10, 9, 8, 7, 6, 5, 4, 3, or 2 nm and at least 2, 3, 4, 5, 6, 7, 8, 9,10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 150, 200, 250, 300, 400, 500,or 750 nm. Nanopores useful in the invention typically range inlongitudinal dimension from 1-1000 nm, e.g., at most 750, 500, 400, 300,250, 200, 150, 100, 90, 80, 70, 60 50, 40, 30, 20, 10, 9, 8, 7, 6, 5, 4,3, or 2 nm and at least 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60,70, 80, 90, 100, 150, 200, 250, 300, 400, 500, or 750 nm. The dimensionsof the nanopore employed will depend on the type of polymer being probedand the conditions of the polymer solution.

Individual polymer molecules may be induced to traverse the aperture bya variety of mechanisms, e.g., diffusion, electrophoretic force forcharged polymers, electroosmotic flow, hydrodynamic pressure, magneticforce for polymers labeled with a magnetic moiety, optical trapping,mechanical force (e.g., from an atomic force microscope), and molecularmotors, e.g., ribosomes or enzymes such as exonucleases, polymerases,and helicases. This method enables alternative probing mechanisms andapplications including the study of molecular structure, e.g.,conformation, and sequencing. As the polymer is traversing the pore,transport properties of the carrying fluid or the polymer itself aremonitoring to determine the conformation of the polymer. Exemplarytransport properties include current, conductance, resistance,capacitance, charge, concentration, optical properties (e.g.,fluorescence and Raman scattering), and chemical structure.

The methods may be used to study any polymer whose movement through asuitably sized pore can be monitored. Polymers may be naturallyoccurring or synthetic. Exemplary polymers include nucleic acids (e.g.,DNA and RNA), proteins, polysaccharides, lipids, and synthetic polymers.

A typical apparatus of the invention includes a voltage-biased nanopore,fabricated in a suitable configuration, e.g., a silicon nitridemembrane. Alternative methods of inducing polymer traversal through thenanopore are described herein. In this embodiment, the membraneseparates two chambers of conducting electrolyte solution. The onlyelectrical conduction path from one chamber to the other passes throughthe nanopore. For double stranded DNA (ds DNA), transverse andlongitudinal dimensions of the pore are smaller than the moleculepersistence length, 50 nm for ds DNA, and the transverse dimension ofthe pore is larger than the ˜2 nm cross sectional size of the molecule.In one example, a nanopore having a transverse dimension of 10 nm of theinvention offers the new ability to observe folding in DNA. Smallerpores, e.g., solid-state nanopore and hemolysin pores having atransverse dimension of 3 nm, do not allow the passage of a folded dsDNA molecule, while other constrictions recently demonstrated are muchlarger than the persistence length of ds DNA and so do not restrict thepassage of DNA to a discrete set of measurable conformations. Aschematic of a typical experimental setup is shown in FIG. 1 b.

The solid state nanopore microscope and method of the invention enablesan interpretation of the time histories of individual molecules—andtheir structures—as they pass through the nanopore, in terms of thecorresponding highly modulated individual events. The nanopore apparatusand method of the invention thereby enables the resolution of multiplefeatures on a single molecule without a priori knowledge of thefeature's characteristics, and to observe new phenomena, like molecularfolding, binding, hybridization, and pairing, by means that have notbeen available in narrower existing biological pores. This significantlyaugments previous work showing that biological pores can distinguishbetween molecules whose chemical structures provide selective binding toa biological pore, and work that shows biological pores can trap andsense the spontaneous disassociation of carefully prepared DNA hairpinsthat are frustrated from translocating the biological pore in theirassociated form. The solid state pores of the invention provide a newway to study the conformations, e.g., folding, binding, hybridization,and pairing configurations, of single long chain molecules, thedifferences between chemically identical molecules in a statisticalensemble, and induced changes in molecular structure that, because ofenergy restrictions, do not occur typically in solution.

A further advantage of solid-state pores is the ability it provides forarticulating the nanopores with electrically conducting electrodes. Suchelectrodes can allow electronic tunneling and near field optical studiesof translocating molecules that are confined in a nanopore. Applyingthese new physical local interactions to molecules translocating throughnanopores can provide local single molecule spectroscopies not affordedby measurement of ionic current alone and offer a means of increasinglongitudinal resolution, possibly to the single-base level for DNA,allowing for extremely rapid sequencing of long molecules.

The ability to determine the conformation of polymers in solution hasseveral uses. For example, the methods of the invention may be used tosurvey a plurality of polymers in a solution to determine theconformational distribution of the population. In addition,conformational changes caused by an intervention can be studied. Forexample, a chemical species, e.g., drugs, ions, oliogomers, surfactants,nucleotide probes and primers, cofactors, enzyme substrates, and otherpolymers, may be added to the solution containing the polymer beingstudied, and a change in conformation can be used to monitor the effectsof the species on the polymer, e.g., binding, hybridization, pairing,denaturation, stabilizing a particular conformation, or other inducedconformation change. Such studies may be employed for drug discovery(e.g., by assaying for candidate binding compounds) and proteomics.Non-chemical interventions, e.g., a temperature change, magnetic field,light, or voltage, may also be employed to determine the effects onconformation. In addition, as the method monitors the conformation asthe polymer traverses an aperture, the relative, or absolute, locationof conformation may be ascertained, e.g., to determine the location of aconformation or changes in conformation or to determine the location ofbinding of a chemical species, e.g., as in probe or primer hybridizationto a nucleic acid. The methods may also be used to monitor the chemicalmakeup or purity of a population of polymers, e.g., the concentration ofa desired polymer or the chemical structure of a polymer, e.g., branchedor linear. The methods of the invention may also be repeated using, forexample, nanopores of different sizes to further probe one or morepolymers.

Detection

Time-dependent transport properties of the aperture may be measured byany suitable technique. The transport properties may be a function ofthe liquid used to transport the polymer, solutes (e.g., ions) in theliquid, the polymer (e.g., chemical structure of the monomers), orlabels on the polymer. Exemplary transport properties include current,conductance, resistance, capacitance, charge, concentration, opticalproperties (e.g., fluorescence and Raman scattering), and chemicalstructure.

Desirably, the transport property is current. Suitable methods fordetecting current in nanopore systems are known in the art, for example,as described in U.S. Pat. Nos. 6,746,594, 6,673,615, 6,627,067,6,464,842, 6,362,002, 6,267,872, 6,015,714, and 5,795,782 and U.S.Publication Nos. 2004/0121525, 2003/0104428, and 2003/0104428. Inanother embodiment, the transport property is electron flow across theaperture, which may be monitored by electrodes disposed adjacent thenanopore.

Fabrication of Nanopores

Any nanopore of the appropriate size may be used in the methods of theinvention. Nanopores may be biological, e.g., proteinaceous, orsolid-state. Suitable nanopores are described, for example, in U.S. Pat.Nos. 6,746,594, 6,673,615, 6,627,067, 6,464,842, 6,362,002, 6,267,872,6,015,714, and 5,795,782 and U.S. Publication Nos. 2004/0121525,2003/0104428, and 2003/0104428. Solid-state nanopores can be fabricatedwith arbitrary size apertures, enabling the study of single molecules ina vast category of polymers in solution, including RNA, hybridized DNA,proteins, and synthetic polymers. An apparatus based on a solid-statenanopore in accordance with the invention provides distinct differencesand advantages over extant biopore detectors. For example, for ds DNAmolecules whose transverse size is ˜2 nm, a hemolysin biopore cannottranslocate such a large diameter molecule. Furthermore, because oftheir physical robustness, solid-state nanopores may well be used tostudy molecules at extremes of temperature, voltage, and pH conditionsthat would destroy biopore-membrane systems.

An exemplary method for fabricating solid-state membranes is the ionbeam sculpting method described in Li et al. Nature 2001, 412:166. Theion beam sculpting process as described herein allows structures to befabricated with desired nanometer scale dimensions from solid statematerials like silicon nitride. Solid-state encompasses both organic andinorganic materials including, but not limited to, microelectronicmaterials, insulating materials such as Si₃N₄, Al₂O₃, and SiO, organicand inorganic polymers such as polyamide, plastics such aspolytetrafluoroethylene, or elastomers such as two-componentaddition-cure silicone rubber, and glasses, although there is nospecific limitation to the materials that may be used according to theinvention.

The manipulation of matter at the nanometer scale is important for manyelectronic, chemical, and biological advances, but conventional solidstate fabrication methods do not typically reproducibly achieve 10⁻⁹meter dimensional control. The ion beam sculpting process overcomes thelimitations of conventional fabrication processes to provide a methodfor precisely controlling nanoscale feature fabrication, specificallywith the use of low energy ion beams. Ion beam sculpting control inaccordance with the invention is found to reveal surprising atomictransport phenomena that occur in a variety of materials and geometries,leading to discoveries of control techniques.

Ion beam sculpting in accordance with the invention can be employed forfabricating a wide range of nanoscale features, including, e.g.,molecular scale holes and apertures, or nanopores, in a solid statematerial, e.g., a thin solid state membrane. Nanopores can serve tolocalize molecular scale electrical junctions and switches and functionas masks to create other small scale structures. Solid state nanoporescan also function in a manner analogous to membrane channels in livingsystems, serving as extremely sensitive electromechanical devices forregulating electrical potential, ionic flow, and molecular transportacross a membrane. In accordance with the invention, controlled ion-beamsculpting has been experimentally employed to produce a robustelectronic detector consisting of a single nanopore in a Si₃N₄ membrane,capable of registering single DNA molecules in aqueous solution.

When ions are directed to a material surface from an ion beam, a numberof processes are understood to occur. In one such process, a sputteringprocess, atomic-scale erosion occurs at the material surface, removingapproximately one atom from the surface for every incident ion. Becauseof this phenomena, as material is removed from a solid stale surface,e.g., a Si₃N₄ surface, which has been processed to contain a bowl-shapedcavity on its opposite surface, as shown in FIG. 6 a, top, the flatsurface will ultimately intercept the bottom of the bowl shaped cavity,forming a nanopore, as shown in FIG. 6 a, bottom. Production of ananopore in this manner requires knowledge of precisely when to stop theion sputtering erosion process. The apparatus shown in FIG. 6 bimplements a feedback-controlled ion sputtering system that counts theions transmitted through the opening pore and extinguishes the erosionprocess at an appropriate time corresponding to a desired pore size. Itis preferred that the apparatus also be operated to control a number ofprocessing parameters found to be important to the ion beam sculptingprocess, including sample temperature; ion beam duty cycle, defined asthe time the beam is on, divided by the sum of the times the beam is onand off, for a pulsed beam; and the instantaneous ion beam flux, F, inions nm⁻²s⁻¹ when the beam is directed to the eroding material.

A 0.1 μm diameter bowl-shaped cavity was fabricated in a free-standingSi₃N₄ membrane supported on a silicon frame, as shown in FIG. 6 a. Toproduce a molecular-scale nanopore, the sample was ion beam sculptedusing 3-keV Ar⁺ ions in the apparatus described above and shown in FIG.6 b. Surprisingly, experiments on this sample at room temperature didnot yield the expected result; a nanopore did not open even afterexcessively long ion beam exposure. The cause for this was discovered byion beam sculpting a membrane containing a through-hole, rather than abowl-shaped cavity. As the sample with a through-hole was exposed to anion beam at room temperature in the apparatus of FIG. 6 b, thetransmitted ion counting rate clearly decreased with increasing ion beamexposure, as shown in FIG. 7 a, suggesting that the hole was closingrather than opening. The incident ion beam was switched off when thecounting rate fell to 40 counts s⁻¹, as shown in FIG. 7 a, inset.

Transmission electron microscope (TEM) images of the hole before andafter the ion beam exposure, as shown in FIGS. 7 b and 7 c, revealedthat the hole size had indeed been reduced from about 60 nm to about 1.8nm by the growth of a thin membrane of a thickness of about 10 nm, asdeduced from electron microscopy. With sufficient ion beam exposure inthe apparatus of FIG. 6 b, the nanopore completely closed, and the ioncount correspondingly was found to fall to zero. This experiment led toa discovery that during exposure of a pore to an ion beam, there must bein addition to ion sputter erosion a lateral atomic flow of matter intothe pore by mass transport, stimulated by the ion beam. That this is asurface, or near-surface phenomenon is strongly suggested by computersimulations showing that ion beam energy is deposited within less thanabout 5 nm of the sample surface.

It has been found that the flow of matter to a developing or closingnanopore in the apparatus of FIG. 6 b is temperature-dependent, as shownin the plot of FIG. 8, where an increasing number of transmitted ionscorresponds to an opening (developing) nanopore and a decreasing numberof transmitted ions corresponds to a closing nanopore. A transitionbetween pore opening and pore closing is found at about 5° C. under theion beam conditions of FIG. 8. When pore area is plotted as a functionof ion beam dose rather than ion beam exposure time, as shown in FIG. 9,the slope of the data reveals that for continuous beam exposure (thegray trace of FIG. 9) the efficiency of pore closing per incident ion isclearly greater at low fluxes than at high fluxes. The plot of FIG. 9also shows that a pulsed beam (the black data points) closes pores moreefficiently than does a continuous ion beam at the same instantaneousflux.

The invention provides a model of the ion beam sculpting processes andtheir process parameter dependencies just described, for enablingcontrol of the sculpting processes. Solutions to analytical expressionsof the model, as-obtained with appropriate parameter values for a givensculpting process, can be employed in accordance with the invention toproduce prespecified nanoscale features in a precise, predictablemanner, and in open-loop fashion, i.e., without the need for closed loopion counting rate feedback control like that employed in the system ofFIG. 6 b. As explained in detail below, the invention provides arecognition that the sputtering and mass transport phenomena discussedabove compete during an ion beam sculpting process. The controlmethodology of the invention provides the ability to control thesephenomena such that one process can dominate over the other in a mannerthat produces a desired nanoscale feature or geometry.

The parameters employed by the analytical model expressions generallydepend on the properties of the material being ion beam sculpted, e.g.,the specific material and material defects and doping impurities, aswell the local environment around the sculpting process, the temperatureof the material, the incident ion species, ion flux, and ion energy, andother parameters that characterize the incident ion beam. It isrecognized in accordance with the invention that the process parameterstherefore are to be adjusted based on a particular ion beam sculptingapplication to achieve desired process results, in the manner describedbelow. For example, it is understood that the charge state of the ionbeam can impact ion beam sculpting parameters. Positive, neutral, ornegative ions can be employed in accordance with the invention toproduce a desired charge state between adatoms, described below, thatare produced during the sculpting process. Similarly, it is understoodthat the ambient gas of the sculpting process can impact sculptingparameters. Chemical reactivity of gas species can be catalyzed by theion beam, resulting in removal or addition of surface adatoms and/orcreation or elimination of surface defect traps.

For clarity, the following discussion is directed to a process modelbased specifically on ion beam sculpting of a nanopore. As explained indetail below, however, the invention is not limited to such. Theanalytical process model expressions provided by the invention can beadjusted to control formation of a wide range of geometries, e.g., slitsor irregularly-shaped holes, trenches, or other geometry, or featuressuch as lithographic mask features, ion beam doping profiles accompaniedby mass transport, or buried layer profiles. There is no fundamentalgeometric symmetry or pattern to which the process control model islimited. Whatever geometry or feature is being formed, it is thenanoscale control of that geometry by the process of the invention thatis universally applicable.

As explained above, the model employed by the invention for use incontrolling ion beam sculpting is based on a recognition that distinctprocesses are likely to compete during the sculpting. Considering ionbeam sculpting involving a nanopore, a first such process tends to openthe pore and is understood to likely be driven by ion beam-sputtererosion of a pore edge. This erosion process is understood to bedominant at low temperatures and high ion beam fluxes. Establishedsputtering phenomenology can be employed for most applications toaccount for and control sculpting processes that are dominated bysputtering in this regime.

A second, competing process tends to cause motion of matter, i.e., masstransport, and can operate to a degree necessary for closing the pore.Without being bound to theory, it is understood that more than one viewcan explain this phenomenon. A first theory understood in accordancewith the invention takes the view that a very thin, e.g., about 5nm-thick, stressed viscous surface layer may be created by the energyand matter deposited on a material surface by an ion beam. An enhancedcollective motion, driven by a reduced viscosity and/or enhanced stressowing to implantation effects or surface tension, may cause the layer torelax, whereby material is transported across a surface.

Although this “reduced viscosity” model has merit, in accordance withthe invention a preferred ion beam sculpting control model reflects aprocess theory in which incident ions create as well as annihilateexcess, independent, and mobile species such as adatoms, ad-dimers,ad-molecules, molecular clusters, and surface vacancies that are presentat the surface of a material exposed to an ion beam. For basicapplications, it is understood to be reasonable to assume a singlemobile species which, for simplicity, will here be called an “adatom.”The changing concentration of surface adatoms, C(r,t), is modeled inaccordance with the invention as a function of distance, r, the radialcoordinate, and time, t, as being governed by a two dimensionaldiffusion equation:

$\begin{matrix}{{{\frac{\partial}{\partial t}{C\left( {r,t} \right)}} = {{FY}_{1} + {D{\nabla^{2}C}} - \frac{C}{\tau_{trap}} - {{FC}\; \sigma_{c}}}},} & \left( {M{.1}} \right)\end{matrix}$

where C is the concentration of adatoms on a two-dimensional surface,r=(x,y) is the radial surface position, t is time, F is the ion flux, Y₁is the number of adatoms created per incident ion, D is the adatomsurface diffusivity, τ_(strap) the average lifetime of an trap is adatombefore thermally-activated adatom annihilation occurs at a surfacedefect, and σ_(c) is the cross-section for adatom annihilation byincident ions. With this expression, it is found that ∂C/∂t depends on ageneration rate, resulting from the ion flux and number of createdadatoms, a transport factor, driving the adatom transport by diffusion,and two annihilation factors, resulting from surface defects and theincident ion beam itself Annihilation of adatoms also occurs at the poreedge as the pore is filled and is treated as a boundary condition forexpression M.1. FIG. 10 illustrates these mechanisms captured in themodel.

The first and last terms on the r.h.s. of expression M.1 reflect anunderstanding provided by the invention that each incident ion resets asurface patch of area σ_(c) to an adatom concentration Y₁/σ_(c) that isindependent of its previous state. The presence of a nanopore in thematerial being subjected to an ion flux is represented by adding anadatom sink at the nanopore edge, for a nanopore radius R, and by addingthe second term on the r.h.s. to model long-range diffusion to the poreedge. Adatoms annihilated at the nanopore boundary are turned into new,stable matter at the boundary.

The magnitudes of the parameters Y₁, D, τ_(trap), and σ_(c) can beestimated for a given ion beam sculpting application from experiencewith suitable materials and can be determined by independentexperiments, e.g., a matrix of pore-closing experiments, preferablyincluding both steady state and transient conditions. It is recognizedin accordance with the invention that the values of these parameters canbe manipulated by adjusting not only temperature, ion beam flux, and ionbeam energy, but also by adjusting the ambient gas species and pressure,ion species, material properties, e.g., concentrations of traceimpurities on the material surface, and material defects and impuritydoping. The parameters are therefore treated here as being adjustable toenable precise control of the ion beam sculpting process for a givenapplication.

By comparison with the r.h.s. third term of expression M.1, the averagelifetime before ion impingement-induced adatom annihilation isτ_(ion)=1/(Fσ_(c)). The effective surface lifetime τ in the presence ofboth annihilation mechanisms is then given as:

$\begin{matrix}{\frac{1}{\tau} = {\frac{1}{\tau_{trap}} + {F\; \sigma_{c}}}} & \left( {M{.2}} \right)\end{matrix}$

It is understood that under some circumstances, one of the final r.h.s.two terms of expression M.1 will be insignificant compared to the other,but this may not necessarily always be the case, and is not required forthe analysis of the invention. An additional annihilation mechanism,adatom annihilation by joining with other adatoms and precipitating intoislands, is not represented in expression M.1 for simplicity so thatthis partial differential equation is linear, rather than nonlinear, forease of solution. It is understood, however, that applications for whichthis annihilation channel cannot be neglected are more precisely modeledwith the addition of another term to the r.h.s. of expression M.1 thatwould be proportional to −C^(n)τ_(island), where n is the number ofadatoms in the critical island (the island that's just big enough to bemore likely to grow than to shrink), and τ_(island) is a characteristictime constant for island formation. Thermal generation of adatoms,thermal desorption into the vacuum, and deposition from the vapor havealso been neglected but can be readily incorporated when necessary for agiven application.

Expression M.1 expresses an understanding that far from a nanopore,steady ion irradiation creates a spatially uniform adatom concentrationC_(SS)=FY₁τ. The pore boundary, or nanopore edge, is taken to be a“perfect sink” for adatoms, which are there transformed to a thin layerof accumulating matter that accounts for pore closure. If the nanoporeedge is taken as a sink for adatoms then the adatom supersaturationdrops as the nanopore edge is approached. Expression M.1 implies thatthe normalized difference, n(r,t), between C_(SS) and C(r,t), given asn(r,t)≡(C_(SS)−C(r,t))/C_(SS), obeys a diffusion equation as:

$\begin{matrix}{\frac{\partial{n\left( {r,t} \right)}}{\partial t} = {{D{\nabla^{2}n}} - \frac{n}{\tau}}} & \left( {M{.3}} \right)\end{matrix}$

The assumption that the pore boundary is a “perfect sink” for adatomsimplies that the adatom concentration, C, vanishes at the pore boundary(of radius R). This is the simplest boundary condition that accounts fora net accumulation of adatoms at the pore, and thus for closure. It isrecognized in accordance with the invention, however, that because ofits interaction with the ion beam, the pore boundary could be a netsource of surface vacancies and still produce this pore-closing effectif vacancies, rather than adatoms, dominate surface transport. Theinvention is therefore not limited to an adatom “perfect sink” boundarycondition. An alternative boundary treatment contemplated by theinvention employs a surface accommodation velocity to describe a partialsink for adatoms at the pore boundary, in a manner analogous to surfacerecombination velocity factors employed in semiconductor modeling ofcharge carriers interacting with surfaces.

Solutions for the spatial adatom concentration profile predicted by theabove model, under a quasi-stationary approximation in which theleft-hand side. of expression M.1 is set to zero, which is justifiedwhen the adatom concentration profile adjusts rapidly to changes in R,yield a spatially uniform steady-state adatom supersaturation far fromthe pore, decaying over a characteristic distance X_(m) to zero at thenanopore edge.

Because adatoms are being removed everywhere on the surface of amaterial exposed to an ion beam, as well as being created by the ionbeam, adatoms created within a distance X_(m) of the pore edge are morelikely to diffuse to and close the pore than be annihilated by incidentions; the opposite is true of adatoms created farther away. X_(m)therefore decreases with increasing flux. Obtaining Y_(p), the effectivecross section for sputter-erosion from the pore edge, from relevant dataobtained at low temperature, where diffusion is expected to beinsignificant, and taking Y₁, the number of adatoms created per incidention, to be of order unity, then for a material thickness of 10 nm, themodel yields the solid curves in FIG. 9 for each incident flux given, ata temperature of about 28° C., a temperature experimentally verified tocause pores to close. From this data, a value of D of about 10³ nm²s⁻¹is extracted, using a linear fit, with σ of about 0.1 nm² as areasonable estimate. The model therefore predicts that the maximumdistance, X_(m), from which adatoms are likely to diffuse to and close apore is linearly proportional to the adatom diffusivity, the traplifetime, the ion beam flux, and the cross section for adatomannihilation, as:

$\begin{matrix}{\frac{1}{X_{m}^{2}} = {\frac{1}{D\; \tau_{trap}} + {\frac{\sigma}{D}F}}} & \left( {M{.4}} \right)\end{matrix}$

and a linear relation is indeed observed (see inset to FIG. 9). X_(m)thus is found to represent a characteristic distance from the pore edgewithin which adatoms are more likely to reach the pore than beannihilated by traps or ion beam flux erosion. Adatoms beyond X_(m) aremore likely to be annihilated before they reach the pore.

As the ion beam flux is increased, the number of adatoms is increased,but the distance from which adatoms can diffuse to and close a pore isreduced. As the average lifetime of an adatom, due to surface defects,is increased, the maximum adatom diffusion distance also increases. Asthe temperature is increased, the diffusivity, and correspondingly, themaximum adatom diffusion distance, is increased. With the analyticalunderstanding of these relationships provided by the invention, thismodel enables an ability to prescribe a minimum distance, X_(m), ofmaterial that must be provided around a starting nanopore to providesufficient material for closing of the nanopore to a desired finalradius R under given processing conditions, and enables adjustment ofprocessing conditions to accommodate a given maximum diffusion distanceX_(m).

The adatom flux, or current, j, at any location r is given by

j(r)=−D∂C/∂r  (M.5)

with r the radial coordinate, and the concentration gradient evaluatedat the edge of the nanopore (r=R) providing the adatom flux j(R) intothe nanopore. Additionally, scraping of material off the edge of thenanopore, tending to open the pore, is accounted for by a characteristiccross section for sputter-erosion from the pore edge.

If each adatom reaching the nanopore fills the pore by a volume Q,thereby reducing the extent of the pore, then the nanopore closing rateis predicted by a volume balance given as:

$\begin{matrix}{{\frac{}{t}\left( {\pi \; R^{2}H} \right)} = {2\; \pi \; R\; {\Omega \left( {{{- j}\; (R)} + {FY}_{p}} \right)}}} & \left( {M{.6}} \right)\end{matrix}$

where Y_(p) is an effective cross section for sputter-erosion from thepore edge, H is the thickness of the film that is formed by filling inthe nanopore, and Ω is the atomic volume. Substituting expression M.5for the adatom current j(R) results in

$\begin{matrix}{{\frac{}{t}\left( {\pi \; R^{2}} \right)} = {{- \frac{2\pi \; \Omega \; {RF}}{H}}\left( {{Y_{1}X_{m}\frac{K_{1}\left( \frac{R}{X_{m}} \right)}{K_{0}\left( \frac{R}{X_{m}} \right)}} - Y_{p}} \right)}} & \left( {M{.7}} \right)\end{matrix}$

where K₀ and K₁ are modified Bessel functions of the second kind.

This expression enables ion beam sculpting control, for a given set ofprocess parameters characteristic of an ion beam environment, to producea nanopore of a desired radius R. For example, it is found from thismodel that pore closing is enhanced with increasing temperature. Thiscan be accounted for by a thermally activated adatom diffusioncoefficient.

In accordance with the control method of the invention, expression M.7can be employed to specify R_(max), the radius of the largest pore thatcan be closed under any particular set of processing conditions. R_(max)increases with increasing temperature and with decreasing flux. At asufficiently high temperature and sufficiently low flux, R_(max) becomesinfinite, a scenario that determines the conditions under which an openpore can be closed. The radius R_(max) is

$\begin{matrix}{{{Y_{1}X_{m}\frac{K_{1}\left( \frac{R}{X_{m}} \right)}{K_{0}\left( \frac{R}{X_{m}} \right)}} - Y} = 0} & \left( {M{.8}} \right)\end{matrix}$

With X_(m), Y₁, and Y_(p) provided as constants, the ratio of

$\frac{K_{1}\left( \frac{R}{X_{m}} \right)}{K_{0}\left( \frac{R}{X_{m}} \right)}$

gets smaller with increasing R, so that at R═R_(max) and above, the porecan no longer close. Analysis of this expression thereby enablesadjustment of processing conditions to produce a desired R_(max).

It has been observed empirically that the thickness, H, of a growingmembrane or film produced as a nanopore is closed depends on the rate ofclosing, d(πR²)/dt, where R is the radius of the nanopore. Higher poreclosing rates result in thinner films than lower pore closing rates. Inaddition, higher ion beam energies result in thicker films than lowerion beam energies. Based on the expressions given above, the inventionprovides the ability to prescribe a film thickness by selecting ion beamsculpting process conditions that result in a corresponding pore closingrate and ion beam energy.

As explained above, it is understood in general in accordance with theinvention that different regions of the perimeter of anarbitrarily-shaped aperture will also open and close according toexpressions M.1 through M.3. In addition, expressions M.4 through M.8can be generalized in an obvious manner to remove the cylindricalsymmetry which is assumed in the example given here, to enable modelingand process control of arbitrarily-shaped features. The invention istherefore not limited to a particular feature geometry.

Time dependent solutions of the adatom diffusion model are employed inaccordance with the invention to describe a sculpting process employinga pulsed ion beam having a selected duty cycle. In order to modelconditions when the incident ion beam is turned off, a steady statecondition is assumed. That is, the ion beam flux is set to F=0, and theinitial concentration of the adatoms on the surface is given, for thenanopore example above, as:

$\begin{matrix}{{C\left( {r,{t = 0}} \right)} = {C_{SS}\left\lbrack {1 - \frac{K_{0}\left( \frac{r}{X_{m}} \right)}{K_{0}\left( \frac{R}{X_{m}} \right)}} \right\rbrack}} & \left( {M{.9}} \right)\end{matrix}$

where C_(SS), is the steady state adatom concentration far from thepore; so that expression M.1 becomes

$\begin{matrix}{{\frac{\partial}{\partial t}{C\left( {r,t} \right)}} = {{D{\nabla^{2}C}} - \frac{C}{\tau_{trap}}}} & \left( {M{.10}} \right)\end{matrix}$

Assuming as boundary conditions for the adatom concentration, C:

$\begin{matrix}{{{C\left( {R,t} \right)} = 0}{{C\left( {{b = {NX}_{m}},t} \right)} = {C_{SS}^{\frac{t}{\tau_{trap}}}}}} & \left( {M{.11}} \right)\end{matrix}$

where b is an outer boundary condition, far from the pore edge, i.e.,N>>1. In practical calculations, N=5 was found to be “big enough”, butit is recognized that for some applications, a larger value of N may berequired for increased accuracy.

Solutions to expression M.10 provide time dependent solutions of theadatom concentration on the surface of the sample after the beam is off,as:

$\begin{matrix}{\mspace{79mu} {{{C^{off}\left( {r,t} \right)} = {{C_{SS}\left\lbrack {\frac{\ln \left( \frac{r}{R} \right)}{\ln \left( {b/R} \right)} + {\sum\limits_{n = 1}^{\infty}\; {A_{n}{U_{0}\left( {\alpha_{n}r} \right)}^{{- \alpha_{n}^{2}}{Dt}}}}} \right\rbrack}^{\frac{t}{\tau_{trap}}}}}\mspace{20mu} {where}{A_{n} = {\frac{\pi^{2}\alpha_{n}^{2}}{2}\frac{J_{0}^{2}\left( {\alpha_{n}R} \right)}{{J_{0}^{2}\left( {\alpha_{n}R} \right)} - {J_{0}^{2}\left( {\alpha_{n}b} \right)}}{\int_{R}^{b}{{r\left\lbrack {1 - \ \frac{K_{0}\left( \frac{r}{X_{m}} \right)}{K_{0}\left( \frac{R}{X_{m}} \right)} - \frac{\ln \left( \frac{r}{R} \right)}{\ln \left( {b/R} \right)}} \right\rbrack}{U_{0}\left( {\alpha_{n}r} \right)}{r}}}}}}} & \left( {M{.12}} \right)\end{matrix}$

where U₀(αr)=J₀(αr)Y₀(αb)−J₀(αb)Y₀(αr) andU₀(α_(n)R)=J₀(α_(n)r)Y₀(α_(n)b)−J₀(α_(n)b)Y₀(α_(n)r)=0 provides theroots of α_(n). J₀, and Y₀ are Bessel functions of the first kind.

The rate at which the area of a pore decreases when the ion beam is offis given as:

$\begin{matrix}{{\frac{\partial}{\partial t}\left( {\pi \; R^{2}} \right)} = \left. {{- \frac{2\pi \; \Omega \; {RF}}{H}}D\frac{\partial C^{off}}{\partial r}} \right|_{r = R}} & \left( {M{.13}} \right)\end{matrix}$

When the ion beam is off, adatoms remain on the surface of the material,but the adatom annihilation channel associated with the incident beamflux is no longer present. Thus, after the beam is extinguished, theremaining adatoms can diffuse to the pore periphery from a greatlyincreased X_(m). This condition can significantly increase theefficiency per ion for pore closing.

In accordance with the invention, expression M.13 can be employed incombination with expression M.2 to predict and then control the rate ofnanopore closing when a pulsed ion beam sculpting process is applied.Specifically, the pulsed ion beam time structure, i.e., the pulse rateand duty cycle, are adjusted in accordance with the invention to achievecontrol over the sign and rate of change of structural dimensions.

It is recognized in accordance with the invention that as with theconditions when the beam is turned off, there is also a transientsolution when the beam is first turned on. This may be important undersome conditions, but it is expected that for most applications, the“beam-on” transient is significantly shorter than the “beam-off”transient and therefore can be ignored. If for a given application suchis not the case, then the “beam-off” transient analysis given above ispreferably extended to the “beam-on” analysis.

The diffusion model employed by the control method of the invention isphenomenological and relies on several idealizations and assumptionsnecessary to compensate for uncertainty in aspects of many microscopicproperties of matter under ion beam exposure. Nevertheless, it isunderstood by the inventors that studies of pulsed and continuous beamexposures at different temperatures, gas ambients, and materialconditions can be employed for a given application in conjunction withthe model to permit the determination of materials-specific parameterslike D, Y₁, σ, and τ_(trap) for the application to enable prespecifiedand precise ion beam sculpting of the material in the production ofuseful nanoscale devices.

Practitioners of ion beam sculpting can use the model provided by theinvention in both quantitative and qualitative ways. That is, by knowingthe qualitative as well as quantitative nature of the solutions to theanalytical model expressions and their dependence on various parametersof the model that are subject to experimental control, these parametersmay be adjusted to achieve desired control over the dimensional controlof structures for large classes of structures. An example would be aqualitative recognition of the ability to increase the rate of shrinkingor even the possibility of shrinking a pore diameter using ion sculptingby increasing the sample temperature or decreasing the incident flux ofincident ions, as well as a quantitative recognition of the degree oftemperature increase or flux decrease required for a given application.In these examples, practitioners are guided to such action by notingthat both of these actions increase the effectiveness of surfacediffusion of adatoms over sputtering, by a temperature enhancement ofthe surface diffusion constant and a reduction in adatom sputteringrespectively.

Other qualitative and quantitative uses of the model includecorrelations between analytical predictions of the model and ancillaryempirical observations. An example of this would be the observation thatnanopores that are reduced to a desired radius more quickly under theion beam sculpting process have a smaller aspect ratio, i.e., length todiameter ratio. Although the model at any given stage of its evolutionmay not contain the details of the process controlling the pore length,it can be used to enhance the pore closing speed and thus improve theaspect ratio.

Thus, as explained above, in accordance with the invention, ion beamsculpting process parameters are adjusted for a given application, basedon the model provided by the invention, to enable prescription ofnanoscale geometries produced by the sculpting process. These parameterswill in general depend on the material being ion sculpted, theenvironment around the structure during the sculpting process,temperature, and on the incident ion species, energy, and otherparameters that characterize the incident ion beam. The incident ionbeam can be supplied as atoms, i.e., neutral ions, ions of a controlledcharge state, molecules or clusters of incident atoms, or indeed anycontrolled energy source. It is recognized that differing modelparameters will be required for the various energy sources. In addition,the invention contemplates the use of multiple energy sources as well asadjustment of the charge state of the material surface at the start andduring the sculpting process.

It is recognized in accordance with the invention that both the surfaceof a structure being ion sculpted and the ion-induced adatoms on thesurface may be highly susceptible to the influence of the environment.By environment is meant a background ambient of a gas like oxygen,hydrogen, sulfur hexafluoride, or other selected gas. As a result theinteraction of these gasses with surface atoms or adatoms, the transportof adatoms and or the removal of surface atoms may be greatly modifiedrelative to the case with the absence of such gasses. Consequently therates and signs of ion sculpting effects will be dramatically modified,and these modifications can be of great utility to the practitioners ofthe ion beam sculpting process. It is also to be recognized that thestate and chemical reactivity of the ambient gas, as well as theexcitation state of the surface or charge state of the surface beingacted upon, may be influenced by the incident ion beam. Means other thanan incident ion beam, such as an electron beam, laser beam, atomic beam,metastable excited atomic beam, mixtures of ion beams, or other energysource, may be used to control the sensitivity of the ion sculptingprocess to the ambient environment in which it is carried out.Adjustment and control of these various influences are recognized inaccordance with the invention to enable flexibility and reproducibilityof prespecified and precise ion beam sculpted geometries of a materialin the production of useful nanoscale devices.

To demonstrate such a device, a nanopore was sculpted in a Si₃N₄membrane for use as a single-molecule electronic detector of DNA.Proteinaceous nanopores, or channels, have been inserted into lipidbilayers in aqueous solutions where they serve as electronic sensors toidentify and characterize single molecules. But proteins in lipidbilayers are labile and the channel diameters they provide cannot easilybe adjusted. Robust, solid-state nanopores, fashioned to any desireddiameter, could yield new data and understanding of transport inconfined spaces, and will make it possible to produce robustsingle-molecule-sensing devices to characterize molecules of DNA andother biopolymers at unprecedented speeds.

Using electrophysiology techniques, a robust, electrically quiet, 5nm-diameter pore was tested with double-stranded DNA. After applying avoltage bias that would draw the negatively charged DNA moleculesthrough the nanopore, diminutions of the ionic current were observed, asshown in FIG. 10, reminiscent of the ionic-current blockages observedwhen single strands of DNA are translocated through the channel formedby α-hemolysin in a lipid bilayer. Because no such blockages were seenduring one hour of monitoring before adding DNA, and because theblockages ceased when the voltage bias was reversed, the blockages areattributed to interactions of individual DNA molecules with thenanopore. The duration of these blockages was on the order ofmilliseconds, and they consistently exhibited current reductions to 88%of the open-pore value. This last value is commensurate withtranslocation of a rod-like molecule whose cross-sectional area is 3-4nm².

The experimental observations, model considerations, and experimentalelectronic device results all described above indicate that the ionbeam-sculpting control method of the invention represents a promisingnew approach to nanoscale fabrication. Specifically, the inventionenables control of sputtering and mass transport processes that competeduring an ion beam sculpting process. With feedback control,reproducibility does not depend on precisely matching all conditions andstarting dimensions. If, however, such can be achieved, then the controlmodel of the invention enables open loop processing without reliance onion rate counting or other feedback control. The invention therefore isnot limited to features or geometries that can accommodate an ionfeedback loop.

The ion beam-sculpting control method of the invention is particularlyuseful for fabricating a wide variety of nanoscale semiconductordevices, masks, and mechanical features, and is not limited forformation of a pore or a through-hole. Slits, trenches, crosses, dopingprofiles, resist patterning, buried layer profiles, and other geometriesand features can be produced. Similarly, a wide range of materials canbe employed, including semiconducting microelectronic materials such asSi, SiO₂, Al, conducting materials, e.g., Al, and others. Furthermore,it is recognized that next-generation ion-source arrays and masktechnologies, combined with multichannel ion detectors, can be employedto enable highly parallel applications of the nanoscale ion beamsculpting control methods of the invention.

Example 1 Evaluation of ds DNA

Methods of the invention will now be discussed relative to DNA analysis.Nanopores employed in this example were fabricated in 25 μm×25 μm freestanding silicon nitride membranes supported by 3 mm×3 mm×0.3 mm siliconsubstrate (100) frames. The 500 nm thick, low stress (˜200 MPa tensile)silicon nitride membrane was deposited by low pressure chemical vapordeposition. Photolithography and anisotropic wet chemical etching ofsilicon were used to create the freestanding SiN membrane. An initial0.1 μm diameter pore was created at the membrane's center using afocused ion beam (FIB, Micrion 9500) machine. The diameter of this largepore was then decreased to molecular size near one surface of themembrane using feedback controlled ion beam sculpting. The finalnanopore resided in a thin, 5-10 nm thick, membrane covering anapproximately 0.1 μm diameter cylindrical aperture extending through thethick silicon nitride membrane below.

Nanopore diameters were determined by transmission electron microscopy.Because TEM projects a three dimensional structure on to a twodimensional plane, the image of the inner edge of the pore actuallyrepresents the minimum projected diameter of the pore wall at any heightand may not correspond to the narrowest physical constriction. Also,because of the inherent inaccuracies of TEM for determining absolutesize and the fact that the pores were not perfectly round, all sizesshould be taken as estimates to within a nanometer of the actual poresize.

FIG. 1 b shows a diagram of the apparatus. The nanopore on the siliconchip separates two chambers filled with buffered salt solution (1M KCl,10 mM TRIS-HCl, pH 8.0). Pre-soaking the chip in isopropanol was foundto aid wetting the pore. The cis chamber, to which DNA molecules areadded, is at the top of the figure and the trans chamber at the bottom.Both chambers are made of PDMS (polydimethylsiloxane) and are equippedwith AgCl electrodes across which a voltage bias is applied duringexperiments. The electrode in the trans chamber is positively biased andconnected to current sensing electronics, while the other electrode isconnected to signal ground.

Double-stranded (ds) DNA with ˜3 kilobase-pairs (kbp) and 10 kbp wereused in this work. The 3 kbp DNA was prepared from pUC19 plasmid (NewEngland Biolabs). The plasmid was cleaved at a single site with SmaIrestriction enzyme to produce blunt-ended linear double-stranded DNA.The purity and quantity of the recovered DNA following phenol extractionwere assessed by agarose gel electrophoresis and UV absorbance. The 10kbp KBA plasmid was linearized by digestion with the SmaI and purifiedfollowing agarose gel electrophoresis using the QIAquick gel extractionkit (QIAGEN Inc., Valencia, Calif.). The DNA was concentrated by ethanolprecipitation as described by Sambrook, et. al. (Molecular Cloning; alaboratory manual, Cold Spring Harbor) and stored dry at 4° C. Dried DNAwas suspended in 10 mM Tris, 1 mM EDTA pH 7.6 (RT) prior to use. Typicalconcentrations of DNA in the cis chamber were ˜10 nM.

Ionic current through the solid-state nanopore was measured and recordedusing an Axopatch 200B integrating patch clamp amplifier system (AxonInstrument) in resistive feedback mode. Signals were preprocessed by a10 kHz low pass filter. Except for the data displayed in FIG. 1 c, whichis a live recording, all data was acquired in event driven acquisitionmode, meaning analog start and stop triggers were used to determine whendata was to be recorded.

In an experimental arrangement in accordance with the invention, openpore ionic conduction was established with 120 mV bias across ananopore. Then DNA was added to the negative cis chamber, and currentblockades appeared in the form of isolated transient reductions incurrent flow through the pore. FIG. 1 c shows part of a current tracerecorded for 3 kb DNA (˜1 μm long) and a 3 nm pore. Each event is theresult of a single molecular interaction with the nanopore and ischaracterized by its time duration t_(d) and its current blockage,ΔI_(b), ˜120 pA. The expected current blockage from a single moleculeblocking the pore is linearly dependent on the cross-sectional area ofthe molecule and independent of the area of the pore, although becausethe blockage current varies inversely with the thickness of the pore,different pores may produce different blockage currents for the samemolecule. Occasionally, the baseline level shifted for very long periodsof time by a magnitude similar to that belonging to the discretetransient molecular event. This was likely due to a single molecule thatbecame “stuck” in the nanopore.

FIG. 2 shows two plots of the density distribution from many transientmolecular events over the parameters <ΔI_(b)> and t_(d). <ΔI_(b)> isdefined as the average value of a current blockade over t_(d)(regardless of the signal's shape). FIG. 2 a is obtained fromexperiments using 10 kbp ds DNA with a 3 nm pore and FIG. 2 b fromexperiments with 10 kbp ds DNA and a 10 nm pore. The voltage bias acrossthe pore in both cases was 120 mV. The coding is keyed to the localdensity of events normalized by the total number of events for eachcase. Although both distributions peak at t_(d) ˜300-400 μsec thedistribution in t_(d) is quite broad for the 3 nm pore experiment andmuch sharper for the 10 nm pore experiment. The distribution of eventsin <ΔI_(b)> for the 10 nm pore is much broader than for the 3 nm pore,with larger <ΔI_(b)> events showing a definite trend towards havingsmaller values of t_(d). FIG. 2 b also shows evidence for attractiveinteractions between different molecules that very occasionally pair upto provide single translocation events for two connected molecules.These appear as a “ghost” structure at twice the expected translocationtimes. Although very few, these events form a separate cluster clearlyseen in the figure. There are too many of these events to be explainedas a simple consequence of the Poisson distribution of event arrivals.

A visual study of individual events for the 3 nm pore plotted in FIG. 2a shows them all to be simple single level current blockades of the typeat the bottom of FIG. 1 c (see also inset FIG. 4 a). Approximately 60%of the events in 10 nm pore experiments are of this type, but theremainder are more complex (see inset FIG. 4 b). Selecting simple singlelevel events from the 10 nm pore data significantly sharpens thedistribution in both <ΔI_(b)> and t_(d). In FIG. 3, a histogram is shownof t_(d) values for simple events in three experiments using 10 nmpores: 3 kbp ds DNA with 120 mV bias, 10 kbp ds DNA with 120 mV bias,and 10 kbp ds DNA with 60 mV bias. The 10 kbp DNA is seen to takeslightly more than 3 times longer to negotiate the pore than the 3 kbpDNA at the same bias. Reducing the bias by a factor of two approximatelydoubles the translocation time. These observations provide strongevidence that each simple single level event corresponds to a DNAmolecule translocating in single file order through the nanopore underthe influence of electrophoretic forces. The structure of the morecomplex signals confirms this interpretation, as discussed herein.

FIG. 4 a shows the density plot of the simple translocation events for10 kbp DNA passing through the 10 nm pore. The main cluster of events isnarrowly distributed in both <ΔI_(b)> and t_(d). The second cluster isdiscussed below, but note its mean <ΔI_(b)> is twice that of the maincluster, while its mean t_(d) is half Characteristic time recordings ofevents from these two regions of the density plot are shown in theinset.

FIG. 4 b shows a density plot for more complex “multi-level” events thatremain after the simple ones are subtracted. Examples of event timerecordings in this group are shown in the inset. They look like simpleevents on which additional blockade structure has been superimposed. For˜85% of the complex events the additional structure appears at the frontof the event, ˜5% at the rear, 1-2% at both the front and rear, and 5%in the middle. Half of the events with structure in the middle havet_(d)>400 μsec. (More complex structures are also observed in longert_(d) events.)

It is recognized in accordance with the invention that these additionalfeatures are attributable to DNA molecules that are folded on themselvesas they pass through the pore. As overlapping folded parts of a moleculepass through the pore they enhance the current blockade during that partof the event. If the instantaneous current blockade is proportional tothe number of strands of the same molecule in the pore (i.e., one ortwo), one calculates that the average current blockade for the eventwill be inversely proportional to the translocation time t_(d),

<ΔI _(b) >=<ΔI ₀ >t ₀ /t _(d)  (1)

where <ΔI₀> and t₀ are the mean current blockage and translocation timeof a simple event. This simple model, plotted as the dotted line in FIG.4 b, shows excellent agreement with the data. The smaller cluster inFIG. 4 a is thus interpreted as due to molecules that are folded nearlyin the middle of the strand. Residual closed circle plasmid DNA in thesample preparation could presumably contribute to this peak.

More confirmation that complex nanopore signals correspond to eventswhere folded DNA molecules translocate through the pore is provided by astudy of the distribution of instantaneous blockade current magnitudesover all events. Assuming the instantaneous magnitude of the blockedcurrent is in proportion to the instantaneous number of strands of dsDNA in the nanopore, it is expected that the distribution of blockedcurrents taken over many events, in time samples much smaller than anevent duration, shows a quantization of local instantaneous ΔI_(b)values corresponding to 0,1,2, . . . strands of the folded molecule inthe pore at any particular time. A histogram of these sampled values ofΔI_(b) for 10 μsec samples over ˜9500 events (including 200 μsec beforeand after each event) is shown in FIG. 5 a for the 10 kb, 120 mV dataand in FIG. 5 b for the 10 kb, 60 mV data. The expected quantization ofsampled ΔI_(b) values is clearly seen corresponding to zero, one and twomolecule strands occupying the nanopore (note the log scale).Experiments with 50 kbp DNA and a 15-20 nm pore (data not shown) alsoshow three level blockades.

The average speed of polymer DNA molecules translocating through 120 mVbiased 10 nm pores is ˜1 cm/sec. A quantitative understanding of thisresult can involve many complex issues like hydrodynamic interactionsand screenings, electro-osmotic flow in and near the pore, andnon-equilibrium statistical considerations. A simple combination oflikely relevant parameters, derived by equating the electric force onthe charged polymer in the pore to a viscous drag on an effective sphereof radius a on either side of the pore, gives an average translocationspeed of

$\begin{matrix}{v = {C\frac{\sigma \; V_{bias}}{\left( {2a} \right)\left( {6\pi \; \eta} \right)}}} & (2)\end{matrix}$

where σ is the linear charge density on the molecule, η the viscosity ofthe solution, V_(bias) the pore voltage bias, and C is a factor of orderunity accounting for the complex issues mentioned above. Setting a tothe persistence length of DNA (which implies statistical loss ofeffective drag force beyond that distance) and assuming a charge of e/3per phosphate, it is found that C˜1/2 brings equation (2) in line withthe experimental observations. This crude result suggests thatunderstanding translocation speed may well require only a mesoscopicfluid dynamical description without the need for invoking strongchemically specific complex interactions between molecule and pore. Theagreement also strengthens the notion that the observed signalscorrespond to molecular translocations.

The observed structured events provide additional compelling evidence infavor of translocation. The quantization of current blockage levelsshows that molecules must be completely threading the pore (if moleculeswere partially blocking the pore, one would expect a continuous range ofblockade currents corresponding to different degrees of pore occlusion).The large electric force (8 kT/nm for 120 mV bias) on a ds DNA moleculein the pore ensures that a molecule that fully enters the pore willtranslocate. Finally, the fact that deeper blockages correspond toshorter events and the good agreement of the data with equation (1) areconsistent only with folded molecules translocating the pore.

Thus, the technique and apparatus provided by the invention enables thedetection of the presence of polymer, e.g., DNA, molecules as well asthe detection and observation of the translocation of individualmolecules through a solid state nanopore.

The majority of leading edge folds might be expected to result from amolecule initially encountering the pore at some distance from its endwith the electrophoretic force from the pore forcing a fold as thetranslocation starts. Simple energetic considerations using the chargeon the molecule and its elastic constant show that this is quitepossible for the electric fields and pore sizes employed experimentally.This does not explain the trailing edge folds which are here ascribed tothe pre-existing state of the molecule (before translocation).

Other Embodiments

All publications, patents, and patent applications mentioned in thisspecification are herein incorporated by reference to the same extent asif each independent publication or patent application was specificallyand individually indicated to be incorporated by reference.

While the invention has been described in connection with specificembodiments thereof, it will be understood that it is capable of furthermodifications and this application is intended to cover any variations,uses, or adaptations of the invention following, in general, theprinciples of the invention and including such departures from thepresent disclosure that come within known or customary practice withinthe art to which the invention pertains and may be applied to theessential features hereinbefore set forth, and follows in the scope ofthe appended claims.

Other embodiments are in the claims.

1. A method for determining the conformation of a nucleic acid, saidmethod comprising the steps of: (a) providing an apparatus comprising:(i) a solid state membrane having a nanopore sized to allow passage ofsaid nucleic acid in said conformation; (ii) first and second fluidreservoirs separated by said membrane and fluidically connected via saidnanopore; and (iii) a detector capable of detecting time-dependentchanges in transport properties of said nanopore; (b) placing saidnucleic acid in said first reservoir; (c) causing said nucleic acid totraverse said nanopore; and (d) measuring said transport properties ofsaid nanopore over time to determine the conformation of said nucleicacid.
 2. The method of claim 1, wherein said nucleic acid is doublestranded or single stranded.
 3. The method of claim 2, wherein saidnucleic acid is DNA.
 4. The method of claim 2, wherein said nucleic acidis RNA.
 5. The method of claim 1, wherein said transverse dimension ofsaid nanopore is at least 4 nm.
 6. The method of claim 1, wherein saidtransverse dimension of said nanopore is at least 10 nm.
 7. The methodof claim 1, wherein said transverse dimension of said nanopore is atleast 15 nm.
 8. The method of claim 1, wherein a longitudinal dimensionof said nanopore is between 1-1000 nm.
 9. The method of claim 1, whereinsaid conformation comprises secondary, tertiary, or quaternary structureformed from binding of a chemical species to said nucleic acid.
 10. Themethod of claim 9, wherein changes in said transport properties overtime are indicative of whether said chemical species is bound to ordissociated from said nucleic acid.
 11. The method of claim 9, furthercomprising determining the location of binding of said chemical speciesto said nucleic acid.
 12. The method of claim 9, wherein said chemicalspecies comprises a nucleic acid probe or nucleic acid primer.
 13. Amethod for evaluating the effects of an intervention on the conformationof a nucleic acid, said method comprising the steps of: (a) providing anapparatus comprising: (i) a solid state membrane having a nanopore sizedto allow passage of said nucleic acid in said conformation; (ii) firstand second fluid reservoirs separated by said membrane and fluidicallyconnected via said nanopore; and (iii) a detector capable of detectingtime-dependent changes in transport properties of said nanopore; (b)providing transport properties of said nanopore over time of saidnucleic acid in the absence of said intervention, wherein changes insaid transport properties over time are indicative of the conformationof said nucleic acid in the absence of said intervention; (c) placingsaid nucleic acid in said first reservoir; (d) applying saidintervention; (e) causing said nucleic acid to traverse said nanopore;(f) measuring said transport properties of said nanopore over time,wherein changes in said transport properties over time are indicative ofthe conformation of said nucleic acid in the presence of saidintervention; and (g) comparing the transport properties of saidnanopore over time from steps (b) and (f) to determine the effect ofsaid intervention on the conformation of said nucleic acid.
 14. Themethod of claim 13, wherein said intervention comprises a chemicalspecies.
 15. The method of claim 14, wherein said chemical species is acandidate binding compound, a denaturant, a nucleic acid probe, or anucleic acid primer.
 16. The method of claim 13, wherein saidintervention comprises a change in temperature.
 17. The method of claim13, wherein said nucleic acid is double stranded or single stranded. 18.The method of claim 17, wherein said nucleic acid is DNA.
 19. The methodof claim 17, wherein said nucleic acid is RNA.
 20. The method of claim13, wherein said transverse dimension of said nanopore is at least 4 nm.21. The method of claim 13, wherein said transverse dimension of saidnanopore is at least 10 nm.
 22. The method of claim 13, wherein saidtransverse dimension of said nanopore is at least 15 nm.
 23. The methodof claim 13, wherein a longitudinal dimension of said nanopore isbetween 1-1000 nm.
 24. The method of claim 13, furthering comprisesrepeating steps (d)-(f), wherein the intervention in the repetition ofstep (d) is changed in type or extent.